Hi Math StackExchange,
I have a large time-dependent matrix that has fluctuating values on the diagonal and constant off-diagonal values. Suppose I have diagonalized the matrix with some initial diagonal. Is there a way to approximate the eigenvalues and eigenvectors of a new matrix with the same off-diagonal values and (slightly) different diagonal values without re-diagonalizing it from scratch? The physical situation here is a Hamiltonian with fluctuating vibrational frequencies and constant vibrational couplings.
Thank you!